/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2009

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef HYPERCUBE_GRAPH_H

 #define HYPERCUBE_GRAPH_H

 #include <vector>

 #include <lemon/core.h>

 #include <lemon/assert.h>

 #include <lemon/bits/graph_extender.h>

 ///\ingroup graphs

 ///\file

 ///\brief HypercubeGraph class.

 namespace lemon {

   class HypercubeGraphBase {

   public:

     typedef HypercubeGraphBase Graph;

     class Node;

     class Edge;

     class Arc;

   public:

     HypercubeGraphBase() {}

   protected:

     void construct(int dim) {

       LEMON_ASSERT(dim >= 1, "The number of dimensions must be at least 1.");

       _dim = dim;

       _node_num = 1 << dim;

       _edge_num = dim * (1 << (dim-1));

     }

   public:

     typedef True NodeNumTag;

     typedef True EdgeNumTag;

     typedef True ArcNumTag;

     int nodeNum() const { return _node_num; }

     int edgeNum() const { return _edge_num; }

     int arcNum() const { return 2 * _edge_num; }

     int maxNodeId() const { return _node_num - 1; }

     int maxEdgeId() const { return _edge_num - 1; }

     int maxArcId() const { return 2 * _edge_num - 1; }

     static Node nodeFromId(int id) { return Node(id); }

     static Edge edgeFromId(int id) { return Edge(id); }

     static Arc arcFromId(int id) { return Arc(id); }

     static int id(Node node) { return node._id; }

     static int id(Edge edge) { return edge._id; }

     static int id(Arc arc) { return arc._id; }

     Node u(Edge edge) const {

       int base = edge._id & ((1 << (_dim-1)) - 1);

       int k = edge._id >> (_dim-1);

       return ((base >> k) << (k+1)) | (base & ((1 << k) - 1));

     }

     Node v(Edge edge) const {

       int base = edge._id & ((1 << (_dim-1)) - 1);

       int k = edge._id >> (_dim-1);

       return ((base >> k) << (k+1)) | (base & ((1 << k) - 1)) | (1 << k);

     }

     Node source(Arc arc) const {

       return (arc._id & 1) == 1 ? u(arc) : v(arc);

     }

     Node target(Arc arc) const {

       return (arc._id & 1) == 1 ? v(arc) : u(arc);

     }

     typedef True FindEdgeTag;

     typedef True FindArcTag;

     Edge findEdge(Node u, Node v, Edge prev = INVALID) const {

       if (prev != INVALID) return INVALID;

       int d = u._id ^ v._id;

       int k = 0;

       if (d == 0) return INVALID;

       for ( ; (d & 1) == 0; d >>= 1) ++k;

       if (d >> 1 != 0) return INVALID;

       return (k << (_dim-1)) | ((u._id >> (k+1)) << k) |

         (u._id & ((1 << k) - 1));

     }

     Arc findArc(Node u, Node v, Arc prev = INVALID) const {

       Edge edge = findEdge(u, v, prev);

       if (edge == INVALID) return INVALID;

       int k = edge._id >> (_dim-1);

       return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1;

     }

     class Node {

       friend class HypercubeGraphBase;

     protected:

       int _id;

       Node(int id) : _id(id) {}

     public:

       Node() {}

       Node (Invalid) : _id(-1) {}

       bool operator==(const Node node) const {return _id == node._id;}

       bool operator!=(const Node node) const {return _id != node._id;}

       bool operator<(const Node node) const {return _id < node._id;}

     };

     class Edge {

       friend class HypercubeGraphBase;

       friend class Arc;

     protected:

       int _id;

       Edge(int id) : _id(id) {}

     public:

       Edge() {}

       Edge (Invalid) : _id(-1) {}

       bool operator==(const Edge edge) const {return _id == edge._id;}

       bool operator!=(const Edge edge) const {return _id != edge._id;}

       bool operator<(const Edge edge) const {return _id < edge._id;}

     };

     class Arc {

       friend class HypercubeGraphBase;

     protected:

       int _id;

       Arc(int id) : _id(id) {}

     public:

       Arc() {}

       Arc (Invalid) : _id(-1) {}

       operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }

       bool operator==(const Arc arc) const {return _id == arc._id;}

       bool operator!=(const Arc arc) const {return _id != arc._id;}

       bool operator<(const Arc arc) const {return _id < arc._id;}

     };

     void first(Node& node) const {

       node._id = _node_num - 1;

     }

     static void next(Node& node) {

       --node._id;

     }

     void first(Edge& edge) const {

       edge._id = _edge_num - 1;

     }

     static void next(Edge& edge) {

       --edge._id;

     }

     void first(Arc& arc) const {

       arc._id = 2 * _edge_num - 1;

     }

     static void next(Arc& arc) {

       --arc._id;

     }

     void firstInc(Edge& edge, bool& dir, const Node& node) const {

       edge._id = node._id >> 1;

       dir = (node._id & 1) == 0;

     }

     void nextInc(Edge& edge, bool& dir) const {

       Node n = dir ? u(edge) : v(edge);

       int k = (edge._id >> (_dim-1)) + 1;

       if (k < _dim) {

         edge._id = (k << (_dim-1)) |

           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));

         dir = ((n._id >> k) & 1) == 0;

       } else {

         edge._id = -1;

         dir = true;

       }

     }

     void firstOut(Arc& arc, const Node& node) const {

       arc._id = ((node._id >> 1) << 1) | (~node._id & 1);

     }

     void nextOut(Arc& arc) const {

       Node n = (arc._id & 1) == 1 ? u(arc) : v(arc);

       int k = (arc._id >> _dim) + 1;

       if (k < _dim) {

         arc._id = (k << (_dim-1)) |

           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));

         arc._id = (arc._id << 1) | (~(n._id >> k) & 1);

       } else {

         arc._id = -1;

       }

     }

     void firstIn(Arc& arc, const Node& node) const {

       arc._id = ((node._id >> 1) << 1) | (node._id & 1);

     }

     void nextIn(Arc& arc) const {

       Node n = (arc._id & 1) == 1 ? v(arc) : u(arc);

       int k = (arc._id >> _dim) + 1;

       if (k < _dim) {

         arc._id = (k << (_dim-1)) |

           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));

         arc._id = (arc._id << 1) | ((n._id >> k) & 1);

       } else {

         arc._id = -1;

       }

     }

     static bool direction(Arc arc) {

       return (arc._id & 1) == 1;

     }

     static Arc direct(Edge edge, bool dir) {

       return Arc((edge._id << 1) | (dir ? 1 : 0));

     }

     int dimension() const {

       return _dim;

     }

     bool projection(Node node, int n) const {

       return static_cast<bool>(node._id & (1 << n));

     }

     int dimension(Edge edge) const {

       return edge._id >> (_dim-1);

     }

     int dimension(Arc arc) const {

       return arc._id >> _dim;

     }

     int index(Node node) const {

       return node._id;

     }

     Node operator()(int ix) const {

       return Node(ix);

     }

   private:

     int _dim;

     int _node_num, _edge_num;

   };

   typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;

   /// \ingroup graphs

   ///

   /// \brief Hypercube graph class

   ///

   /// HypercubeGraph implements a special graph type. The nodes of the

   /// graph are indexed with integers having at most \c dim binary digits.

   /// Two nodes are connected in the graph if and only if their indices

   /// differ only on one position in the binary form.

   /// This class is completely static and it needs constant memory space.

   /// Thus you can neither add nor delete nodes or edges.

   ///

   /// This type fully conforms to the \ref concepts::Graph "Graph concept".

   /// Most of its member functions and nested classes are documented

   /// only in the concept class.

   ///

   /// \note The type of the indices is chosen to \c int for efficiency

   /// reasons. Thus the maximum dimension of this implementation is 26

   /// (assuming that the size of \c int is 32 bit).

   class HypercubeGraph : public ExtendedHypercubeGraphBase {

     typedef ExtendedHypercubeGraphBase Parent;

   public:

     /// \brief Constructs a hypercube graph with \c dim dimensions.

     ///

     /// Constructs a hypercube graph with \c dim dimensions.

     HypercubeGraph(int dim) { construct(dim); }

     /// \brief The number of dimensions.

     ///

     /// Gives back the number of dimensions.

     int dimension() const {

       return Parent::dimension();

     }

     /// \brief Returns \c true if the n'th bit of the node is one.

     ///

     /// Returns \c true if the n'th bit of the node is one.

     bool projection(Node node, int n) const {

       return Parent::projection(node, n);

     }

     /// \brief The dimension id of an edge.

     ///

     /// Gives back the dimension id of the given edge.

     /// It is in the range <tt>[0..dim-1]</tt>.

     int dimension(Edge edge) const {

       return Parent::dimension(edge);

     }

     /// \brief The dimension id of an arc.

     ///

     /// Gives back the dimension id of the given arc.

     /// It is in the range <tt>[0..dim-1]</tt>.

     int dimension(Arc arc) const {

       return Parent::dimension(arc);

     }

     /// \brief The index of a node.

     ///

     /// Gives back the index of the given node.

     /// The lower bits of the integer describes the node.

     int index(Node node) const {

       return Parent::index(node);

     }

     /// \brief Gives back a node by its index.

     ///

     /// Gives back a node by its index.

     Node operator()(int ix) const {

       return Parent::operator()(ix);

     }

     /// \brief Number of nodes.

     int nodeNum() const { return Parent::nodeNum(); }

     /// \brief Number of edges.

     int edgeNum() const { return Parent::edgeNum(); }

     /// \brief Number of arcs.

     int arcNum() const { return Parent::arcNum(); }

     /// \brief Linear combination map.

     ///

     /// This map makes possible to give back a linear combination

     /// for each node. It works like the \c std::accumulate function,

     /// so it accumulates the \c bf binary function with the \c fv first

     /// value. The map accumulates only on that positions (dimensions)

     /// where the index of the node is one. The values that have to be

     /// accumulated should be given by the \c begin and \c end iterators

     /// and the length of this range should be equal to the dimension

     /// number of the graph.

     ///

     ///\code

     /// const int DIM = 3;

     /// HypercubeGraph graph(DIM);

     /// dim2::Point<double> base[DIM];

     /// for (int k = 0; k < DIM; ++k) {

     ///   base[k].x = rnd();

     ///   base[k].y = rnd();

     /// }

     /// HypercubeGraph::HyperMap<dim2::Point<double> >

     ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));

     ///\endcode

     ///

     /// \see HypercubeGraph

     template <typename T, typename BF = std::plus<T> >

     class HyperMap {

     public:

       /// \brief The key type of the map

       typedef Node Key;

       /// \brief The value type of the map

       typedef T Value;

       /// \brief Constructor for HyperMap.

       ///

       /// Construct a HyperMap for the given graph. The values that have

       /// to be accumulated should be given by the \c begin and \c end

       /// iterators and the length of this range should be equal to the

       /// dimension number of the graph.

       ///

       /// This map accumulates the \c bf binary function with the \c fv

       /// first value on that positions (dimensions) where the index of

       /// the node is one.

       template <typename It>

       HyperMap(const Graph& graph, It begin, It end,

                T fv = 0, const BF& bf = BF())

         : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf)

       {

         LEMON_ASSERT(_values.size() == graph.dimension(),

                      "Wrong size of range");

       }

       /// \brief The partial accumulated value.

       ///

       /// Gives back the partial accumulated value.

       Value operator[](const Key& k) const {

         Value val = _first_value;

         int id = _graph.index(k);

         int n = 0;

         while (id != 0) {

           if (id & 1) {

             val = _bin_func(val, _values[n]);

           }

           id >>= 1;

           ++n;

         }

         return val;

       }

     private:

       const Graph& _graph;

       std::vector<T> _values;

       T _first_value;

       BF _bin_func;

     };

   };

 }

 #endif